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#### Search: #### Pochhammer

Function: pochhammer (<n>, <x>) The Pochhammer symbol. For nonnegative integers <n> with `<n> <= pochhammer_max_index`, the expression `pochhammer (<x>, <n>)` evaluates to the product `<x> (<x> + 1) (<x> + 2) ... (<x> + n - 1)` when `<n> > 0` and to 1 when `<n> = 0`. For negative <n>, `pochhammer (<x>, <n>)` is defined as `(-1)^<n> / pochhammer (1 - <x>, -<n>)`. Thus ```          (%i1) pochhammer (x, 3);
(%o1)                   x (x + 1) (x + 2)
(%i2) pochhammer (x, -3);
1
(%o2)               - -----------------------
(1 - x) (2 - x) (3 - x)```

To convert a Pochhammer symbol into a quotient of gamma functions, (see Abramowitz and Stegun, equation 6.1.22) use `makegamma`; for example

```          (%i1) makegamma (pochhammer (x, n));
gamma(x + n)
(%o1)                     ------------
gamma(x)```

When <n> exceeds `pochhammer_max_index` or when <n> is symbolic, `pochhammer` returns a noun form.

```          (%i1) pochhammer (x, n);
(%o1)                         (x)
n```

There are also some inexact matches for `pochhammer`. Try `?? pochhammer` to see them.

```(%o1)                                true
(%i2) ```

### Related Examples

##### pochhammer

pochhammer (10,1 );

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##### pochhammer

pochhammer (1.5, 3);

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##### pochhammer

pochhammer (1.5, 3);

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##### pochhammer

pochhammer (-2,4);

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pochhammer ( 2,100);

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##### pochhammer

pochhammer (2,4 );

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##### pochhammer

pochhammer (-N, 0);

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##### pochhammer

pochhammer ( -5,2);

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##### pochhammer

pochhammer (x, 3);

pochhammer (-5, 5);

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##### pochhammer

pochhammer ( -5,2);

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